I wroteF = P Q L/c (1/b - 1/a)because there is an absolute value and I know what makes that positive and didn't wrote the 4 lines of code to automatise the process in quick and dirty mode. Program is already a mess and needs refactoring.

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and this is interesting, but I'm still wondering about the effect of L = cavity height, which this doesn't address.

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MeasuredFrequency = c/L; therefore L = c / MeasuredFrequency;

But I don't buy that. L need only have units of length. That's why I asked you to test L = cavity height .

For me L is just a convenient way to input the frequency. The conversion factor, c, is unlikely to see great changes soon, and taking the inverse makes no difference further than negating the exponents. It is convenient precisely because it has natural units of length and can mix easily with a and b.

edit: I like to see F = P/c times dimensionless_factor because for the only both experimentally proven and theoretically understood propellantless propulsion (you know, my friend, the photon rocket) we have this beautiful (but also hopelessly scant) formula F = P/c times one.

Alright there is a big fudge factor of 13100, that looks like the ballpark of Q values, but note that it doesn't move, it is still 13100 even with Q values going from 5900 to 50000. First and fourth values 1.16 and 0.71 ratio 1.63, no more relative deviation than MiHsC 0.50 and 0.87 ratio 1.74

To me this is indicative that this former formula is as good at predicting an effect independent of Q than the later at indicating a linear dependency on Q. Introducing a constant is a lot of information added to fit the data (considering the sparsity of data the risk of overfitting is great) but it also discards two parameters Q and Lambda (or frequency) so is simpler in this respect. What would 13100 stand for ? Let me see... something vaguely around the squared inverse of the fine structure constant for instance ?

Do I have an agenda ? Of course I have an agenda. But this isn't numerology.And this can wait until tomorrow.

Alright there is a big fudge factor of 13100, that looks like the ballpark of Q values, but note that it doesn't move, it is still 13100 even with Q values going from 5900 to 50000. First and fourth values 1.16 and 0.71 ratio 1.63, no more relative deviation than MiHsC 0.50 and 0.87 ratio 1.74

To me this is indicative that this former formula is as good at predicting an effect independent of Q than the later at indicating a linear dependency on Q. Introducing a constant is a lot of information added to fit the data (considering the sparsity of data the risk of overfitting is great) but it also discards two parameters Q and Lambda (or frequency) so is simpler in this respect. What would 13100 stand for ? Let me see... something vaguely around the squared inverse of the fine structure constant for instance ?

Do I have an agenda ? Of course I have an agenda. But this isn't numerology.And this can wait until tomorrow.

Well, obviously

(a-b)^2/(ab) = ( (a/b -1) + (b/a -1))

or

(a-b)^2/(ab) = ( (RR - 1) + (1/RR - 1))

which is a symmetrized measure of the distance from unity of the relative ratio (RR = a / b) between the two diameters of the bases of the truncated cone. (This measure is zero for RR =1 and it goes to Infinity either as RR --> Infinity or as RR --> 0)

Alright there is a big fudge factor of 13100, that looks like the ballpark of Q values, but note that it doesn't move, it is still 13100 even with Q values going from 5900 to 50000. First and fourth values 1.16 and 0.71 ratio 1.63, no more relative deviation than MiHsC 0.50 and 0.87 ratio 1.74

To me this is indicative that this former formula is as good at predicting an effect independent of Q than the later at indicating a linear dependency on Q. Introducing a constant is a lot of information added to fit the data (considering the sparsity of data the risk of overfitting is great) but it also discards two parameters Q and Lambda (or frequency) so is simpler in this respect. What would 13100 stand for ? Let me see... something vaguely around the squared inverse of the fine structure constant for instance ?

Do I have an agenda ? Of course I have an agenda. But this isn't numerology.And this can wait until tomorrow.

Well, obviously

(a-b)^2/(ab) = ( (a/b -1) + (b/a -1))

or

(a-b)^2/(ab) = ( (AR - 1) + (1/AR - 1))

which is a symmetrized measure of the distance from unity of the aspect ratio (AR = a / b) between the two diameters of the bases of the truncated cone. (This measure is zero for AR =1 and it goes to Infinity either as AR --> Infinity or as AR --> 0)

And I am sorry, but I don't see anything here but someone quoting someone else. Can you show me the original source statement, or better, proof? I can show you the original source statement that L is the Unruh wavelength here:

In MiHsC the inertial mass (mi) is modified as mi=m(1-L/4T) where m is the unmodified mass, L is the Unruh wavelength determined by the acceleration, and T is the Hubble distance

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What if the resonant cavity walls acted like a Hubble horizon, especially for Unruh waves of a similar length (as they are in this case)? Then the inertial mass of the photons would increase towards the cavity's wide end, since more Unruh waves would fit there, since mi=m(1-L/2w), where w is the cavity width. The force carried by the photons then increases by this factor as they go from the narrow end (width w_small) towards the wide end (width w_big). The force difference between ends is

dF = (PQ/c)*((L/w_big)-(L/w_small)) = (PQ/f)*((1/w_big)-(1/w_small)).

If we consider L to be the RF drive wavelength, then how do we justify talking about the Unruh effect and how it may interact with the photons to cause the excessive thrust? If L is not the RF wavelength then it could be just about anything although it seems that it could be related to cavity dimensions. Ask Prof. M, but I think it doesn't have to be.

If we consider L to be the RF drive wavelength, then how do we justify talking about the Unruh effect and how it may interact with the photons to cause the excessive thrust? If L is not the RF wavelength then it could be just about anything although it seems that it could be related to cavity dimensions. Ask Prof. M, but I think it doesn't have to be.

OK point well taken. You are correct, that is the Unruh wavelength explanation.

Here is the practical problem.

There are an infinite number of Unruh wavelengths, and they have an energy spectrum.

I imagine that there is an Unruh wavelength that best fits. Which Unruh wavelength to take? Assume that the longest wavelength that fits is the most energetic? That fits in what lengh? (Which way do the wavelengths fit in the cavity? along the longitudinal axis of revolution of the cone?)

How do we decide what "L" to use in the analysis? For NASA Eagleworks? For Shawyer?

If it is an Unruh wave, it is initiated by acceleration of the cavity walls. Which walls are accelerated by the RF photons? I think it is the end circular walls. That is, the RF waves resonate parallel to the axis of symmetry. So the Unruh waves also propagate parallel to the axis of symmetry.

What are the Unruh wave wavelengths? They are either constrained by the cavity end separation or they are unique to the end from which they propagate. They need not propagate from both ends, that is, one end could act as a horizon and emit a wave while the other does not but this seems unlikely. It seems more likely that the ends emit Unruh waves of different wavelength. If they are not coupled to each other, that is. But if they are coupled then cavity dimensions play a role in fixing the wavelength?

But don't get to hung up on the actual value of the wavelength. If it exists at all, then imagine what the photon must see as it approached the wall. Nothing of course, the photon is moving at the speed of light so can only see behind and to angles to the rear. But from the Unruh effect, that wall is hot so like a blind cat on a hot stove, the photon departs with more energy than it arrived with. Its frequency or its mass is up-shifted as is its momentum. How much? I think that gets us back to the Unruh effect. And what is really up-shifted? Its inertial mass of course because that is what put us on this path in the first place.

If we consider L to be the RF drive wavelength, then how do we justify talking about the Unruh effect and how it may interact with the photons to cause the excessive thrust? If L is not the RF wavelength then it could be just about anything although it seems that it could be related to cavity dimensions. Ask Prof. M, but I think it doesn't have to be.

OK point well taken. You are correct, that is the Unruh wavelength explanation.

In my equationless style, I'm still not on board with the HYPOTHETICAL Unruh wave explanation. Further, since there must be an integral number of these faith based waves in the cavity, and since resonance is THE operative factor, there should have been, from the summa cavea arachis at any rate, much tighter control over the bandwidth of the wavelength sent to the device.

What you guys are talking about is not making sense. Not sayin' you're talking nonsense. You're still talking about the copper geometry as having some special refractive index which works at 1.9xxx GHz, using waves which have not been seen.

If we consider L to be the RF drive wavelength, then how do we justify talking about the Unruh effect and how it may interact with the photons to cause the excessive thrust? If L is not the RF wavelength then it could be just about anything although it seems that it could be related to cavity dimensions. Ask Prof. M, but I think it doesn't have to be.

OK point well taken. You are correct, that is the Unruh wavelength explanation.

In my equationless style, I'm still not on board with the HYPOTHETICAL Unruh wave explanation. Further, since there must be an integral number of these faith based waves in the cavity, and since resonance is THE operative factor, there should have been, from the summa cavea arachis at any rate, much tighter control over the bandwidth of the wavelength sent to the device.

What you guys are talking about is not making sense. Not sayin' you're talking nonsense. You're still talking about the copper geometry as having some special refractive index which works at 1.9xxx GHz, using waves which have not been seen.

As can be seen, Shawyer b and both Jauns have L values that fit the within cavity dimensions, which is around 0.38 m. Unfortunately by forcing the fit above I have forced all of the errors from the experiments and the analysis into the values of L.

I wonder if this advances our search. Two of the 7 experiments are satisfied with L = cavity height, and one has L < cavity height. The only other one that is close is the Brady outlier. I don't know what to make of that. I do know that I should use Prof. M's original formula, not the one with the constant factor. Maybe later.

Its later. Prof. M's 1-D equation is not satisfied with L chosen to force fit the experimental data. That is, of course the numbers are calculated but the values of L are all to small to relate to the cavity. In fact, except for Shawyer a, they are all smaller than the RF wavelength. Close, but smaller. Well, the Brady outlier is much smaller, not even close to the RF wavelength.

Is there a chance that the formula above, using ab(1/b-1/a)^2, an area like expression, could end up being similar to Prof. M's 3-D model that he is working on? That is, could

dF = Q*L* P/c ab(1/b-1/a)^2

be a 3-D representation of the MiHsC model. I guess I should ask Prof. M himself.

....I wrote a small program to generate some exhaustive search on formulas upon the relevant factors then sieving those formulas that fit the available data. This is completely theoretically agnostic but it does check for dimensional consistency (as far as kg m s units are concerned). The search goes on for any product of the terms a b L Q P F c (respectively w_big w_small wavelength=c/Freq Power Thrust Speed_of_light) with all possible whole exponents from -2 to +2 (going through 0) and tries to equal 1 (with the experimental data). It also tries an "extended" term (exterm) that is a combination of 2 homogeneous terms ( that is a b or L ) at any power -2 to +2 through any of the operators sum difference geometrical_average, and then to any power -2 to +2.This does cover the formula by McCulloch but not Shawyer's.

The sieve goes like that : use the formula on each of the seven data points to generate a value hopefully close to 1. If it is not close to 1 but close to a given value (say 2) for all the data points then we have a constant fudge factor, but if the standard deviation around it is small this is still interesting : a strong relation still holds between the terms in such formula. The mean and deviation are calculated in log space, that is a mean of 0 is a best result (formula gives values around 1) while a mean of -1 or +1 says the formula gives values e (=2.72) times too low or too big.

I would like to see how the formula parameters behave with this outlier taken out.

Yes. The Brady outlier certainly shows us something but it doesn't show us how the thruster works ideally. It shows how it works when something goes wrong. That's important to know but not useful in the context of discovering the ideal operational model and parameters.

For our purposes now of discovering the ideal operational model and parameters, we should avoid outliers when they have been identified. Once the data is evaluated with Brady b" removed we can consider if perhaps Shawyer a" isa less than ideal case as well.

I would like to see how the formula parameters behave with this outlier taken out.

Yes. The Brady outlier certainly shows us something but it doesn't show us how the thruster works ideally. It shows how it works when something goes wrong. That's important to know but not useful in the context of discovering the ideal operational model and parameters.

For our purposes now of discovering the ideal operational model and parameters, we should avoid outliers when they have been identified. Once the data is evaluated with Brady b" removed we can consider if perhaps Shawyer a" isa less than ideal case as well.

I think that placing this outlier in the data masks the importance of Q.Taking it out of the data may show again the importance of Q.

As @aero states, imagine that this thruster works based on resonance (as was the expectation by all the researchers in the US, UK and China) and that one cannot control the bandwidth adequately at high Q (as pointed out by Ludwick).

Due to frequency drift, one ends up with tests that are in resonance and tests (like the outlier) that drift out of resonance and produce very low experimental force.

To understand the mechanism we have to look at the data with the outlier included (done) and with the outlier excluded.